Trying to create a 3D print of a spray paint stencil and I'm having difficulty joining 'islands'. What I'm doing wrong?
I think the normals on the inside of your main character profiles are flipped .. it would explain the twisting on the bridge. Also remember, to be tidy, Bridge Edge Loops needs an equal number of vertices on both sides.

Try a quick CtrlN 'Make Normals Consistent' on the entire mesh in edit mode.

Have a look to see: in Edit Mode, Properties Region > Mesh Display panel > Normals > Face..

It would probably be easier to create the bridges in the flat, before extruding the thickness of the piece.. you could, instead of using a Boolean, Knife-Project the text down on to a plane, make the bridges, and then extrude.